# Recommended root canal

**Algebra**Level 4

Find the largest possible product \(n\cdot m\) of two distinct positive integers \(n\) and \(m,\) such that the equations \( (x+1)^n=x^n+1\) and \((x+1)^m=x^m+1\) have the same set of complex roots.

**Details and assumptions**

The multiplicities of the roots can, of course, be different, but each root of one equation is a root of the other.